Further results on radar pointing error reduction using discreteextended Kalman filtering

A recently proposed method of reducing target glint errors in radar systems using extended Kalman filtering is further extended with the inclusion of and compensation for clutter effects. A discrete target model and discrete Kalman filter (DKF) are used. Simulation results demonstrating the DKF are presented, and the limits on the effectiveness of the method are investigated. The major advantage of the DKF is that it can be implemented in software in the digital processor of the radar, offering flexibility over continuous time filters. The ability of the filter to reduce clutter effects further demonstrates the usefulness of this technique for radar pointing error reduction     

Tracking an incoming ballistic missile using an extended interval Kalman filter

The important tracking problem by radar of an incoming ballistic missile system, which contains uncertainty in modeling and noise in both dynamics and measurements, is studied. The classical extended Kalman filter (EKF) is no longer applicable to such an uncertain system, and so a new extended interval Kalman filter (EIKF) is developed for tracking the missile system. Computer simulation is presented to show the effectiveness of the EIKF algorithm for this uncertain and nonlinear ballistic missile tracking problem.     

Analytical Steady State Solution for a Kalman Tracking Filter

Analytical expressions are given for the steady state solution to a Kalman tracking filter used in a track-while-scan radar system. The radar sensor measures range and range rate, and both these measurements are utilized in the filter. The solution for range measurements only is obtained as a special case. Graphs are also given which show how the solution depends on different parameters.     

A nonlinear helicopter tracker using attitude measurements

Extended-Kalman-filter-based trackers are discussed for maneuvering helicopters that use body angle and rotor tip-path-plane angle measurements in addition to the usual radar position measurements. Improvements were found in tracker performance when the body rotation and rotor tip-path-plane degrees of freedom were modeled within the extended Kalman filter. Tracker performance was further improved when measurements of body angles and rotor tip-path-plane angles were made available to the tracker     

基于广义Kalman估计的机载雷达高精度控制系统

 研究了在某型现役机载雷达系统中, 采用广义Kalman 滤波器方法来预估目标机的俯仰角和方位角,产生跟踪目标用的雷达天线驱动信号, 替代传统的速率陀螺测量元件来补偿本机机动所造成的扰动的方法,同时对探测信号本身所具有的延迟起到了补偿作用。对目标的运动采用直角坐标系中的Singer 模型描述, 而对测量信号则是应用极坐标系中的描述, 采用广义Kalman 滤波器来完成估计, 即在每一步的估计和控制中对计算测量方程进行线性化结果, 实现两种坐标系的转换。通过应用Matlab/ Simulink 软件对整个系统的建模、设计及仿真研究, 得到了满意的结果。     

Efficient Approximation of Kalman Filter for Target Tracking

A Kalman filter in the Cartesian coordinates is described for a maneuvering target when the radar sensor measures range, bearing, and elevation angles in the polar coordinates at high data rates. An approximate gain computation algorithm is developed to determine the filter gains for on-line microprocessor implementation. In this approach, gains are computed for three uncoupled filters and multiplied by a Jacobian transformation determined from the measured target position and orientation. The algorithm is compared with the extended Kalman filter for a typical target trajectory in a naval gun fire control system. The filter gains and the tracking errors for the proposed algorithm are nearly identical to the extended Kalman filter, while the computation requirements are reduced by a factor of four.     

Tracking a ballistic target: comparison of several nonlinear filters

This paper studies the problem of tracking a ballistic object in the reentry phase by processing radar measurements. A suitable (highly nonlinear) model of target motion is developed and the theoretical Cramer-Rao lower bounds (CRLB) of estimation error are derived. The estimation performance (error mean and standard deviation; consistency test) of the following nonlinear filters is compared: the extended Kalman filter (EKF), the. statistical linearization, the particle filtering, and the unscented Kalman filter (UKF). The simulation results favor the EKF; it combines the statistical efficiency with a modest computational load. This conclusion is valid when the target ballistic coefficient is a priori known.     

Design of a practical tracking algorithm with radar measurements

The extended Kalman filter (EKF) has been widely used as a nonlinear filtering method for radar tracking problems. However, it has been found that if cross-range measurement errors of the target position are large, the performance of the conventional EKF degrades considerably due to nonnegligible nonlinear effects. A new filtering algorithm for improving the tracking performance with radar measurements is developed based on the fact that correct evaluation of the measurement error covariance is possible in the Cartesian coordinate system. The proposed algorithm may be viewed as a modification of the EKF in which the variance of the range measurement errors is evaluated in an adaptive manner. The filter structure facilitates the incorporation of the sequential measurement processing scheme, and this makes the resulting algorithm favorable to both estimation accuracy and computational efficiency. Computer simulation results show that the proposed method offers superior performance in comparison to previous methods. Moreover, our developed algorithm provides some useful insight into the radar tracking problem     

Real-Time Wind Estimation and Tracking with Transponder Downlinked Airspeed and Heading Data

The use of magnetic heading and true air speed measurements made on board civil airplanes to assist in radar tracking is described. The data are telemetered via the air-ground data link of the mode S radar system. A new filter, similar to the first-order Kalman filter, is developed using velocity measurements to bias its prediction equations. This filter follows satisfactorily maneuvers, and estimates, in real time, the wind in the vicinity of the airplane. Finally a scheme is described to remove false data due to data-link corruption.     

Coordinate Conversion and Tracking for Very Long Range Radars

The problem of tracking with very long range radars is studied in this paper. First, the measurement conversion from a radar's r-u-v coordinate system to the Cartesian coordinate system is discussed. Although the nonlinearity of this coordinate transformation appears insignificant based on the evaluation of the bias of the converted measurements, it is shown that this nonlinearity can cause significant covariance inconsistency in the conventionally converted measurements (CM1). Since data association depends critically on filter consistency, this issue is very important. Following this, it is shown that a suitably corrected conversion (CM2) eliminates the inconsistency. Then, initialized with the converted measurements (using CM2), four Cartesian filters are evaluated. It is shown that, among these filters, the converted measurement Kalman filter with second order Taylor expansion (CM2KF) is the only one that is consistent for very long range tracking scenarios. Another two approaches, the range-direction-cosine extended Kalman filter (ruvEKF) and the unscented Kalman filter (UKF) are also evaluated and shown to suffer from consistency problems. However, the CM2KF has the disadvantage of reduced accuracy in the range direction. To fix this problem, a consistency-based modification for the standard extended Kalman filter (E1KF) is proposed. This leads to a new filtering approach, designated as measurement covariance adaptive extended Kalman filter (MCAEKF). For very long range tracking scenarios, the MCAEKF is shown to produce consistent filtering results and be able to avoid the loss of accuracy in the range direction. It is also shown that the MCAEKF meets the posterior Carmer-Rao lower bound for the scenarios considered.     

Real-Time Tracking Filter Evaluation and Selection for Tactical Applications

Five important tracking filters that are often candidates for implementation in systems that must track maneuvering vehicles are compared in terms of tracking accuracy and computer requirements for tactical applications. A rationale for selecting among these filters, which include a Kalman filter, a simplified Kalman filter, an ?-? filter, a Wiener filter, and a two-point extrapolator, is illustrated by two examples taken from the authors' recent experience.     

A three-state Kalman tracker using position and rate measurements

A three-state Kalman tracker is described for tracking a moving target, such as an aircraft, making use of the position and rate measurements obtained by a track-white-scan radar sensor which employs pulsed Doppler processing, such as the moving target detector providing unambiguous Doppler data. The steady-state filter parameters have been analytically obtained under the assumption of white noise maneuver capability. The numerical computations of these parameters are in excellent agreement with those obtained from the recursive Kalman filter matrix equations. The solution for the case when only the range measurements are available is obtained as a special case of this model. Graphs of normalized covariances and gains are presented to illustrate how the solution depends on different parameters     

Velocity Estimation from Position Outputs of a Three-Dimensional Radar

Kalman filtering equations to obtain estimates of velocity from radar position information are defined. In a track-while-scan operation, a three-dimensional radar sensor measures range, bearing, and elevation (r, ?, ?) of an airborne target at uniform sampling intervals of time T. The noisy position measurements are converted to x, y, z coordinates and put through a Kalman filter to obtain x, y, z velocity components. The filtering equations together with steady-state error estimates are given.     

Radar Target Pointing Error Reduction Using Extended Kalman Filtering

A new method of reducing target glint errors in radar systems is presented. The target is modeled as n reflectors whose magnitudes and phases are known. The reflector positions are described by a dynamical model driven by white Gaussian noise. The resulting vibrations of the target reflectors produce glintlike pointing errors in the radar system. An extended Kalman filter is developed to estimate the positions of the target reflectors; this information is used to substantially reduce the pointing error due to glint. Data illustrating this glint reduction is given. The model is extended by the inclusion of clutter effects modeled in the same fashion as the glint phenomenon. The results presented indicate the limits of usefulness of this technique as a function of both receiver noise and relative clutter amplitude.     

Streamlining measurement iteration for EKF target tracking

The estimation problem is defined, and a review of how the linear estimation approach of Kalman filtering is extrapolated to form an extended Kalman filter (EKF), applicable for state estimation in nonlinear systems is presented. A mechanization of an EKF variation known as an iterated EKF, offering improved tracking performance, is treated. A streamlined version of an iterated EKF that has a lesser computational burden (fewer operations per cycle or time step) than prior formulations is offered. A nonlinear filtering application example, to be used as a testbed for this new approach, is described, and the detailed modeling considerations as needed for exoatmospheric random-variable radar target tracking are discussed. The performance of the streamlined mechanization is illustrated in this radar target tracking example, and comparisons are made with the performance of an EKF without measurement iteration     

A Nonlinear Tracker Using Attitude Measurements

The subject of this paper involves tracking the present position of a maneuvering aircraft as well as predicting its future position. A tracking filter is developed that uses aircraft attitude angles (yaw, pitch, roll) in addition to the usual radar measurements. Computer simulation of tracker performance when tracking violently maneuvering aircraft indicates that a dramatic improvement is obtained by using attitude information. The approach taken is to develop a 12-or 15-state extended Kalman filter that models both translational and rotational degrees of freedom. By measuring and estimating attitude it is possible to approximately determine the magnitude and direction of the force system acting on the vehicle and therefore determine vehicle linear acceleration. Knowledge of acceleration is then used to improve the estimate of present and future position of the vehicle being tracked. Simulation of a T-38 aircraft performing a 5 g turn indicates that the new tracker produces maximum trajectory prediction errors that are 36 percent of the errors experienced by more conventional trackers.     

A track filter for reentry objects with uncertain drag

A filter was developed for maintaining track on ballistic missiles whose drag profiles are unknown or deviate significantly from prior predictions. The filter employs an innovative form of a seven-state Kalman filter in which object drag is included as a state to be estimated. Using measurements of range, azimuth, and elevation, the filter can track endo- and exo-atmospheric targets on a wide variety of trajectories without requiring a priori tuning to account for variations in reentry angle, drag history, measurement signal-to-noise ratio, etc. The filter was designed to be implemented at the millimeter wave (MMW) radar (a high-range-resolution, narrow beamwidth, Ka-band radar) located at Kwajalein Missile Range (KMR) in the Marshall Islands. Extensive testing and comparisons using a high fidelity simulation showed the new filter to be robust to a wide variety of trajectories and substantially better than track filters presently used at KMR. The filter was coded to run efficiently in real time, installed at the MMW radar, and successfully used to track an intercontinental ballistic missile (ICBM) with varying drag characteristics through exo-atmospheric and reentry phases. The filter yielded a more accurate and responsive track than possible with the previously used filter on a similar trajectory     

均方意义下三维雷达无偏转换测量误差协方差阵的推导

在以前的研究中,无偏转测量误差协方差阵是基于当前测量值得到的.为了能利用所有历史数据以得到更精确的转换测量误差协方差阵估计,文中在均方意义下,推导了三维雷达的最优无偏转换测量误差协方差阵.     

Sequential nonlinear tracking using UKF and raw range-rate measurements

The three-dimensional (3D) converted measurements filtering (CMF) with both converted position and raw range-rate measurement is proposed to solve the Doppler radar target tracking, where the error between radar-target range and range rate are correlated. Firstly, not using pseudomeasurement constructed by product of range and range rate to reduce the high nonlinearity, the raw range-rate measurements are utilized by unscented Kalman filter (UKF), where the converted errors of the position and the range rate are decorrelated, then linear part (position measurements) and nonlinear part (range-rate measurement) are sequentially processed by Kalman filter (KF) and UKF. Secondly, based on the assumption of small measurement error, the mean and covariance of converted measurement errors are derived by second-order Taylor series expansion. Finally, the influence of the correlated coefficient rho between the range and range rate, and the range-rate noise deviation sigma_r are taken into account and extreme values of rho and sigma_r are used in Monte Carlo simulations. The results show that the proposed method is, in a sense, effective and practical     

FDEKF在反辐射无人机抗目标雷达关机中的应用

基于捷联惯导/反辐射导引头组合抗目标雷达关机制导方案,研究了有限差分卡尔曼滤波(FDEKF)方法在对目标雷达被动定位中的应用。考虑反辐射导引头测角存在非线性特性,提出了一种基于扩展状态变量维数的方法实现了目标状态估计和导引头非线性特性补偿。仿真结果表明,FDEKF是一种具有良好性能的非线性滤波方法,可以代替传统的EKF解决反辐射无人机对目标雷达的被动定位问题。